Solution to the Avogadro constant challenge

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Solution to the Avogadro constant challenge

Jensen, William B.; Meija, Juris

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Analytical and Bioanalytical Chemistry © Crown Copyright in Right of Canada 2010 10.1007/s00216-010-3961-8

Analytical Challenge

Solution to the Avogadro constant

challenge

William B. Jensen1_{and Juris Meija}2

(1) Department of Chemistry, University of Cincinnati, Cincinnati, OH 45221, USA

(2) Institute for National Measurement Standards, National Research Council Canada, 1200 Montreal Road, Ottawa, ON, K1A 0R6, Canada

Email: juris.meija@nrc.ca

The Avogadro constant has long been defined as the number of molecules of a substance in a gram molecular weight [1]. In a modern parlance, it is a fundamental physical constant representing the number of entities comprising 1 mol. It is clear that any modification to the definition of macroscopic (kilogram) or microscopic mass scales (atomic mass) will affect the numerical value of the Avogadro constant. The definition of kilogram has remained unaltered since the very first Conférence Générale des Poids et Mesures in September of 1889, when it was declared that the international prototype of the kilogram “shall henceforth be considered to be the unit of mass,” not so with the definition of the atomic mass scale. In 1803/1805, John Dalton established the first atomic mass scale in which hydrogen was assigned Ar(H) =

1, whereas the current definition sets Ar(12C) = 12. In addition, there

were numerous other scales used during the intervening years (Table1). Though Dalton's H = 1 mass scale was used in chemistry for nearly a century, many of these alternative scales, following a suggestion by Wollaston, employed oxygen as the standard instead—an idea which resurfaced near the end of the nineteenth century as the O = 16 scale. With the discovery of isotopes, the oxygen scale was refined to the16_{O isotope, albeit only among physicists.}

Table 1 Relative atomic mass scales through the centuries

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H = 1 (O = 5.5) Dalton, 1803–5 H = 1 (O = 16) Davy, 1812 O = 10 Wollaston, 1813 O = 1 Thomson, 1813, 1825 O = 100 Berzelius, 1814 O = 4 Griffin, 1834 O = 16 Clarke, 1893 C = 12 Hinrichs, 1893 20th_{century: isotopic mass scale} 16_{O = 16} _{Aston, 1931} 12_{C = 12} _{IUPAC, 1961}

Notations O = 16 or12_{C = 12 describe the relative atomic mass (atomic weight) scale.} When m(E) is the average mass of atoms of element E, the atomic weight of E is given by Ar(E) = m(E)/mu, where muis the atomic mass constant. In the O = 16 scale mu= m(O)/16, whereas mu= m(12_{C)/12 in the}12_{C = 12 scale}

The most recent change in the atomic mass scale occurred during the height of the cold war when the oxygen scale, Ar(16O) = 16, was abandoned in favor of the

current Ar(12C) = 12 by the International Union of Pure and Applied Physics (Ottawa

1960) and by the International Union of Pure and Applied Chemistry (Montreal 1961) [2].

The relative atomic mass of the16_{O isotope in the}12_{C-scale is 15.9949—a difference}

of 0.03% from the “old” value of 16.0000. This shift, in turn, alters the value of the Avogadro constant from 6.024 × 1023_{to 6.022 × 10}23_mol−1_{. This “change” in the}

numerical value of the Avogadro constant can be easily spotted by inspection of twentieth century chemistry textbooks [3].

It may be of interest here to mention an earlier story regarding the value of the Avogadro constant when determination of NAinvolved measurements of lattice

spacing in crystals [4]. In 1919, at a time when wavelengths could not be measured directly, Manne Siegbahn (1924 Nobel Prize in Physics) proposed the 'local' non-SI unit of length for measuring the wavelength of x-rays. A student of Siegbahn, Erik Bäcklin, in his 1928 dissertation showed that wavelengths measured at incidence angles near grazing were 0.2% higher than the equivalent wavelengths measured by traditional crystal diffraction methods. This single discrepancy initially challenged the work of no less than five Nobel laureates-Richards, Bragg, Millikan, Siegbahn, and Compton. By the mid 1930s, however, a mistake was found in Millikan's classic elementary charge measurement due to an error in the value for the viscosity of air.

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Once this was corrected the accepted value of the Avogadro constant dropped by 0.6% [5].

References

1. Perrin JB (1965) Discontinuous structure of matter. In: Nobel lectures, Physics. Elsevier, Amsterdam, pp 1922–1941

2. Holden NE (2004) Chem Int 26:4–7 3. Jensen WB (2010) J Chem Educ (in press) 4. Bassow H (1991) J Chem Educ 68: 273-274 5. Lipson H, Riley DP (1943) Nature 151: 250-250